Version (19.9 KB) by Jan
A faster FILTER and FILTFILT: Speedup factor 2.5 to 25


Updated 20 Jul 2011

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FilterM, FiltFiltM: Fast digital filter

These functions are compatible to MATLAB's FILTER and FILTFILT commands,
but they are faster (see screenshot):
FilterM: 30%-40% of FILTER runtime
FiltFiltM: 4%-20% of FILTFILT runtime

- The dimension to operate on can be specified for FiltFiltM.
- FilterM can process the signal in backward direction. (This is the
main part of the acceleration of FiltFiltM, because it avoids to
reverse the signal two times.)
- For signals of type SINGLE, the intermediate values are stored in
DOUBLE precision to increase the accuracy. The output is converted
to SINGLE again.
- The Signal Processing Toolbox is *not* needed.

Y = FiltFiltM(b, a, X, Dim)
[Y, Zf] = FilterM(b, a, X, Zi, Dim, Reverse)

b, a: Filter parameters as DOUBLE vectors.
X: Signal as DOUBLE or SINGLE vector or array.
Zi, Zf: Initial and final conditions as DOUBLE or SINGLE array.
Optional, default: Zeros.
Dim: Dimension to operate on. Optional, default: 1st non-singelton.
Reverse: Flag to process the signal in reverse direction.
Optional, default: FALSE.
Y: Filtered signal, same size and type as X.
While FilterM filters in forward direction, FiltFiltM processes
the signal forward and reverse direction for a zero phase

To accelerate my FEX submission FiltFiltM, I've implemented a filter as
C-Mex, which works in reverse order. To my surprise this was faster than
running Matlab's FILTER forward, e.g. 3.7 times for a [10000 x 1] vector,
5th order Butterworth filter (Matlab 2009a, WinXP 32 bit, single core).
Therefore I've expanded the Mex such that the direction can be defined
as input. The algorithm is a direct form II transposed structure.
A future version will be mutli-threaded.

Setup the compiler if not done before: mex -setup.
Auto-compilation: Call FilterM without inputs to start the compilation.
A pre-compiled Mex can be downloaded:
Run the unit-tests uTest_FilterM and uTest_FiltFiltM to check validity and speed.

Tested: Matlab 6.5, 7.7, 7.8, WinXP, 32bit
Compiler: LCC2.4/3.8, BCC5.5, OWC1.8, MSVC2008
Assumed Compatibility: higher Matlab versions, Mac, Linux, 64bit

This is faster and more powerful than my former submission "FiltFiltM", which will be removed soon.

Cite As

Jan (2023). FilterM (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2009a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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